Finite Group Databasebeta

← #7898078

Subgroups — #7898078

Order 512.

4295 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic
2#59459C212yesmaximal
3#52274C211yesmaximal, characteristic
4#51602C214yesmaximal
5#51080C214yesmaximal
6#51080C214yesmaximal
7#47727C214yesmaximal
8#46006C212yesmaximal
9#45279C212yesmaximal
10#45279C212yesmaximal
11#45277C212yesmaximal
12#44419C214yesmaximal
13#42825C212yesmaximal
14#42823C212yesmaximal
15#42004C214yesmaximal
16#39978C212yesmaximal
17#39749C211yesmaximal, characteristic
18#39701C212yesmaximal
19#39621C212yesmaximal
20#39621C212yesmaximal
21#39619C212yesmaximal
22#39612C211yesmaximal, characteristic
23#37196C212yesmaximal
24#36466C211yesmaximal, characteristic
25#35937C212yesmaximal
26#35582C212yesmaximal
27#35199C211yesmaximal, characteristic
28#34488C212yesmaximal
29#34328C211yesmaximal, characteristic
30C2×Q82C2212yes—
31C2×#557C2212yes—
32C2×#557C2212yes—
33C2×#557C2211yescharacteristic
34#2863C2212yes—
35#2862C2212yes—
36#2862C2212yes—
37#2859C2211yescharacteristic
38#2859C2212yes—
39#2844C2214yes—
40#2843C2214yes—
41#2811C2214yes—
42#2809C2212yes—
43#2809C2211yescharacteristic
44#2806C2214yes—
45#2806C2214yes—
46#2806C2211yescharacteristic
47#2806C2212yes—
48#2806C2214yes—
49#2806C2214yes—
50#2806C2214yes—
51#2805C2212yes—
52#2805C2211yescharacteristic
53#2805C2214yes—
54#2802C2212yes—
55#2802C2214yes—
56#2802C2214yes—
57#2802C2214yes—
58#2799C2212yes—
59#2792C2214yes—
60#2792C2214yes—
61#2792C2214yes—
62#2791C2212yes—
63#2791C2214yes—
64#2791C2214yes—
65#2774C2214yes—
66#2774C2212yes—
67#2774C2214yes—
68#2755C2214yes—
69#2755C2214yes—
70#2755C2212yes—
71#2755C2214yes—
72#2734C2212yes—
73#2734C2214yes—
74#2734C2212yes—
75#2734C2212yes—
76#2734C2214yes—
77#2734C2212yes—
78#2726C2211yescharacteristic
79#2726C2212yes—
80#2726C2212yes—
81#2726C2214yes—
82#2726C2214yes—
83#2726C2212yes—
84#2726C2214yes—
85#2713C2214yes—
86#2713C2214yes—
87#2713C2214yes—
88#2713C2212yes—
89#2713C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2713C2214yes—
93#2713C2214yes—
94#2713C2214yes—
95#2666C2214yes—
96#2666C2214yes—
97#2666C2214yes—
98#2666C2214yes—
99#2666C2214yes—
100#2660C2214yes—
101#2660C2212yes—
102#2660C2214yes—
103#2660C2212yes—
104#2660C2212yes—
105#2612C2214yes—
106#2612C2214yes—
107#2606C2214yes—
108#2606C2214yes—
109#2605C2214yes—
110#2605C2214yes—
111#2590C2214yes—
112#2590C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2586C2214yes—
116#2586C2214yes—
117#2586C2214yes—
118#2586C2214yes—
119#2586C2214yes—
120#2586C2214yes—
121#2586C2214yes—
122#2584C2214yes—
123#2584C2212yes—
124#2584C2214yes—
125#2584C2214yes—
126#2582C2211yescharacteristic
127#2582C2212yes—
128#2570C2212yes—
129#2570C2212yes—
130#2568C2212yes—
131#2568C2212yes—
132#2568C2211yescharacteristic
133#2567C2212yes—
134#2567C2212yes—
135#2567C2214yes—
136#2565C2212yes—
137#2565C2212yes—
138#2565C2212yes—
139#2552C2212yes—
140#2552C2211yescharacteristic
141#2552C2212yes—
142#2551C2211yescharacteristic
143#2551C2212yes—
144#2551C2212yes—
145#2551C2212yes—
146#2551C2214yes—
147#2551C2214yes—
148#2551C2212yes—
149#2551C2211yescharacteristic
150#2551C2212yes—
151#2550C2214yes—
152#2550C2214yes—
153#2550C2212yes—
154#2550C2212yes—
155#2550C2214yes—
156#2550C2212yes—
157#2550C2214yes—
158#2550C2214yes—
159#2550C2212yes—
160#2550C2212yes—
161#2550C2214yes—
162#2546C2211yescharacteristic
163#2546C2214yes—
164#2546C2214yes—
165#2520C2214yes—
166#2520C2214yes—
167#2520C2214yes—
168#2511C2214yes—
169#2511C2214yes—
170#2509C2212yes—
171#2508C2212yes—
172#2506C2212yes—
173#2462C2214yes—
174#2462C2214yes—
175#2462C2214yes—
176#2462C2214yes—
177#2462C2214yes—
178#2462C2214yes—
179#2453C2212yes—
180#2453C2212yes—
181#2451C2214yes—
182#2451C2214yes—
183#2451C2212yes—
184#2451C2212yes—
185#2451C2212yes—
186#2451C2212yes—
187#2451C2212yes—
188#2451C2212yes—
189#2451C2214yes—
190#2451C2212yes—
191#2451C2214yes—
192#2451C2214yes—
193#2451C2214yes—
194#2451C2214yes—
195#2451C2212yes—
196#2446C2214yes—
197#2446C2212yes—
198#2446C2214yes—
199#2446C2214yes—
200#2402C2212yes—
201#2402C2212yes—
202#2399C2214yes—
203#2399C2212yes—
204#2382C2214yes—
205#2382C2214yes—
206#2371C2214yes—
207#2370C2214yes—
208#2370C2212yes—
209#2370C2214yes—
210#2365C2212yes—
211#2365C2211yescharacteristic
212#2365C2212yes—
213#2365C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2356C2212yes—
217#2356C2212yes—
218#2355C2214yes—
219#2355C2211yescharacteristic
220#2355C2211yescharacteristic
221#2355C2212yes—
222#2351C2212yes—
223#2351C2212yes—
224#2351C2212yes—
225Q8×C4⋊C4C2211yescharacteristic
226Q8×C4⋊C4C2212yes—
227Q8×C4⋊C4C2212yes—
228Q8×C4⋊C4C2211yescharacteristic
229#2336C2214yes—
230#2336C2214yes—
231#2336C2214yes—
232#2331C2214yes—
233#2331C2212yes—
234#2331C2212yes—
235#2330C2212yes—
236#2330C2214yes—
237#2327C2212yes—
238#2327C2212yes—
239#2327C2212yes—
240#2320C2214yes—
241#2320C2212yes—
242#2320C2212yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2212yes—
247C4×C4⋊Q8C2212yes—
248C4×C4⋊Q8C2211yescharacteristic
249C4×#125C2212yes—
250C4×#125C2212yes—
251#2295C2211yescharacteristic
252#2295C2212yes—
253#2295C2212yes—
254#2295C2211yescharacteristic
255#2295C2212yes—
256#2295C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259Q82—48no—
260#557—48no—
261#557—48no—
262#557Q8116yescomplemented
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2314yes—
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#125C2314yes—
291C2×#125C2314yes—
292C2×#125C2314yes—
293C2×#125C2312yes—
294C2×#125C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2312yes—
327#400C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2312yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2312yes—
463#391C2314yes—
464#391C2311yescharacteristic
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2311yescharacteristic
470#391C2314yes—
471#391C2311yescharacteristic
472#391C2311yescharacteristic
473#389C2311yescharacteristic
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2311yescharacteristic
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2311yescharacteristic
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2312yes—
541#389C2312yes—
542#389C2314yes—
543#389C2312yes—
544#389C2311yescharacteristic
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2311yescharacteristic
549#389C2311yescharacteristic
550#389C2312yes—
551#387C2314yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2312yes—
605#387C2314yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2312yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2312yes—
619#387C2314yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2314yes—
624#387C2314yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#384C2312yes—
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2312yes—
633#384C2311yescharacteristic
634#384C2311yescharacteristic
635#384C2312yes—
636#384C2312yes—
637#384C2311yescharacteristic
638#384C2314yes—
639#384C2314yes—
640#384C2312yes—
641#383C2314yes—
642#383C2314yes—
643#383C2314yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#382C2314yes—
655#382C2312yes—
656#382C2314yes—
657#382C2314yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2311yescharacteristic
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707#376C2312yes—
708#376C2312yes—
709#376C2314yes—
710#376C2312yes—
711#376C2314yes—
712#376C2314yes—
713C43C2312yes—
714C43C2312yes—
715C43C2311yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×Q8C2414yes—
724C22×Q8C2414yes—
725C22×Q8C2414yes—
726C22×Q8C2411yescharacteristic
727C4⋊Q8—28no—
728C4⋊Q8—24no—
729C4⋊Q8—28no—
730C4⋊Q8—24no—
731C4⋊Q8—44no—
732C4⋊Q8—44no—
733C4⋊Q8—48no—
734C4⋊Q8—44no—
735C4⋊Q8—44no—
736C4⋊Q8—48no—
737C4⋊Q8—48no—
738C4⋊Q8—48no—
739C4⋊Q8—48no—
740C4⋊Q8—84no—
741C4⋊Q8—84no—
742C4⋊Q8—84no—
743C4⋊Q8—82no—
744C4⋊Q8—82no—
745C4⋊Q8C2×Q818yes—
746C4⋊Q8C2×Q8116yes—
747#125—28no—
748#125—28no—
749#125—48no—
750#125—48no—
751#125—44no—
752#125—44no—
753#125—48no—
754#125—48no—
755#125—84no—
756#125—84no—
757#125C2×Q8116yes—
758#125C2×Q8132yes—
759C4×Q8—24no—
760C4×Q8—28no—
761C4×Q8—24no—
762C4×Q8—24no—
763C4×Q8—28no—
764C4×Q8—28no—
765C4×Q8—48no—
766C4×Q8—48no—
767C4×Q8—44no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×Q8—44no—
771C4×Q8—44no—
772C4×Q8—48no—
773C4×Q8—44no—
774C4×Q8—84no—
775C4×Q8—82no—
776C4×Q8C2×Q8116yes—
777C4×Q8C2×Q818yes—
778C4×Q8C2×Q8116yes—
779C4×Q8C2×Q818yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2411yescharacteristic
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2411yescharacteristic
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2414yes—
917#95C2412yes—
918#95C2414yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998C2×Q8—22no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—22no—
1002C2×Q8—24no—
1003C2×Q8—22no—
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—28no—
1007C2×Q8—28no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—42no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—42no—
1015C2×Q8—41no—
1016C2×Q8—44no—
1017C2×Q8—44no—
1018C2×Q8—44no—
1019C2×Q8—41no—
1020C2×Q8—42no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8C22×Q814yes—
1029C2×Q8C22×Q818yes—
1030C2×Q8C22×Q814yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2512yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—22no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—22no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—41no—
1089C4⋊C4—42no—
1090C4⋊C4—41no—
1091C4⋊C4—42no—
1092C4⋊C4—41no—
1093C4⋊C4—41no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—41no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—42no—
1145C4⋊C4C22×Q814yes—
1146C4⋊C4C22×Q818yes—
1147C4⋊C4C22×Q8116yes—
1148C4⋊C4C22×Q814yes—
1149C4⋊C4C22×Q818yes—
1150C4⋊C4C22×Q818yes—
1151C4⋊C4C22×Q8116yes—
1152C4⋊C4C22×Q8116yes—
1153C4⋊C4C22×Q818yes—
1154C4⋊C42−1+414yes—
1155C4⋊C42−1+414yes—
1156C42—24no—
1157C42—28no—
1158C42—24no—
1159C42—24no—
1160C42—24no—
1161C42—24no—
1162C42—22no—
1163C42—28no—
1164C42—24no—
1165C42—24no—
1166C42—22no—
1167C42—24no—
1168C42—24no—
1169C42—41no—
1170C42—42no—
1171C42—42no—
1172C42—44no—
1173C42—41no—
1174C42—42no—
1175C42—44no—
1176C42—44no—
1177C42—44no—
1178C42—44no—
1179C42—44no—
1180C42—44no—
1181C42—41no—
1182C42—42no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—42no—
1188C42C22×Q818yes—
1189C42C22×Q8116yes—
1190C42C22×Q814yes—
1191C42C22×Q818yes—
1192C42H(5,𝔽2)14yes—
1193C23C2611yescharacteristic
1194Q8—28no—
1195Q8—216no—
1196Q8—44no—
1197Q8—48no—
1198Q8—88no—
1199Q8—82no—
1200Q8—84no—
1201Q8—88no—
1202Q8—88no—
1203Q8—164no—
1204Q8—164no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4C23×Q814yes—
1278C2×C4C23×Q812yes—
1279C2×C4C23×Q814yes—
1280C2×C4C23×Q814yes—
1281C2×C4C23×Q812yes—
1282C2×C4C23×Q814yes—
1283C2×C4C23×Q818yes—
1284C2×C4C23×Q812yes—
1285C2×C4C2×H(5,𝔽2)12yes—
1286C2×C4C2×H(5,𝔽2)12yes—
1287C2×C4C2×H(5,𝔽2)12yes—
1288C2×C4C2×2−1+412yes—
1289C2×C4C2×2−1+414yes—
1290C2×C4C2×2−1+414yes—
1291C2×C4C2×2−1+412yes—
1292C22C24×Q811yescharacteristic
1293C22C22×H(5,𝔽2)11yescharacteristic
1294C22C22×2−1+411yescharacteristic
1295C22C22×2−1+411yescharacteristic
1296C22H(7,𝔽2)11yescharacteristic
1297C222−1+611yescharacteristic
1298C222−1+611yescharacteristic
1299C4—24no—
1300C4—22no—
1301C4—24no—
1302C4—24no—
1303C4—28no—
1304C4—24no—
1305C4—22no—
1306C4—24no—
1307C4—22no—
1308C4—22no—
1309C4—24no—
1310C4—22no—
1311C4—42no—
1312C4—41no—
1313C4—44no—
1314C4—42no—
1315C4—44no—
1316C4—42no—
1317C4—44no—
1318C4—44no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—44no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4#350314yes—
1328C2C2×#350311yescharacteristic
1329C2#6284911yescharacteristic
1330C2#6287811yescharacteristic
1331C2#6294211yescharacteristic
1332C2#6294711yescharacteristic
1333C2Q8×2−1+411yescharacteristic
1334C2#6305811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
262. #557Q8semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#598322
#594592
#522742
#516022
#510802
#477272
#460062
#452792
#452772
#444192
#428252
#428232
#420042
#399782
#397492
#397012
#396212
#396192
#396122
#371962
#364662
#359372
#355822
#351992
#344882
#343282